+---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ | | | | | | | +---+---+---+---+---+---+ +---+---*---+---+ +---+---+---*---+ +---+---+---*---+ | | H | | | | | H | | | | H | +---*===*---+---+ +---*===*===*---+ +---+---*===*---+ | H | | | | H | | | | | H | | +---*===*===*---+ +---*===*===*---+ +---+---*---+---+ | | | H | | | | H | | | H | | +---+---*===*---+ +---*===*===*---+ +---*===*---+---+ | | H | | | H | | | | H | | | +---+---*---+---+ +---*---+---+---+ +---*---+---+---+ ] It is obvious that a board of four squares can only be so divided in one way--by a straight cut down the centre--because we shall not count reversals and reflections as different. In the case of a board of sixteen squares--four by four--there are just six different ways. I have given all these in the diagram, and the reader will not find any others. Now, take the larger board of thirty-six squares, and try to discover in how many ways it may be cut into two parts of the same size and shape. 289.--LIONS AND CROWNS. The young lady in the illustration is confronted with a little cutting-out difficulty in which the reader may be glad to assist her. She wishes, for some reason that she has not communicated to me, to cut that square piece of valuable material into four parts, all of exactly the same size and shape, but it is important that every piece shall contain a lion and a crown. As she insists that the cuts can only be made along the lines dividing the squares, she is considerably perplexed to find out how it is to be done. Can you show her the way? There is only one possible method of cutting the stuff. [Illustration: +-+-+-+-+-+-+ | | | | | | | +-+-+-+-+-+-+ | |L|L|L| | | +-+-+-+-+-+-+ | | |C|C| | | +-+-+-+-+-+-+ | | |C|C| | | +-+-+-+-+-+-+ |L| | | | | | +-+-+-+-+-+-+ | | | | | | | +-+-+-+-+-+-+ ] 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.